Find the mean and variance for the following frequency distribution
Classes         0-10 10-20 20-30 30-40 40-50
Frequencies    5       8        15      16        6

Solution:

Let us draw the frequency table based on the given problem

Class	Frequency fi	Mid-Point (xi)	yi = (xi - 25)/10	yi²	fiyi	fiyi²
0 - 10	5	5	- 2	4	- 10	20
10 - 20	8	15	- 1	1	- 8	8
20 - 30	15	25	0	0	0	0
30 - 40	16	35	1	1	16	16
40 - 50	6	45	2	4	12	24
	50				10	68

Mean,

x = A + [∑⁵_{i = 1} f_iy_i] / N × h

= 25 + 10/50 × 10

= 25 + 2

= 27

Variance,

(σ ²) = h² / N² [N ∑⁵_{i = 1}(f_iy_i)² - (∑⁵_{i = 1}f_iy_i)²]

= (10)²/(50)² [50 × 68 - (10)²]

= 1/25 [3400 - 100]

= 3300/25

= 132

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.2 Question 8

Find the mean and variance for the following frequency distribution Classes         0-10 10-20 20-30 30-40 40-50 Frequencies    5       8        15      16        6

Summary:

The mean and variance for the frequency distribution for the given data are 27 and 132